A comparative study for selecting and using simulation methods of Gaussian random surfaces
A comparative study for selecting and using simulation methods of Gaussian random surfaces
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DOI：
10.1016/j.triboint.2021.107347
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发表时间：
2022-02
影响因子：
6.2
通讯作者：
Yuechan Wang;Abdullah Azam;M. Wilson;A. Neville;A. Morina
中科院分区：
文献类型：
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作者：
Yuechan Wang;Abdullah Azam;M. Wilson;A. Neville;A. Morina
生成高斯随机曲面的传统方法，包括移动平均（MA）时间序列模型与非线性共轭梯度法（NCGM）、二维（2-D）数字滤波器法和谱表示法（SRM），都是在自相关函数（ACF）的自相关长度和截断长度值范围很宽的情况下实现的。计算并比较了模拟表面的ACF、功率谱密度函数（PSDF）和基本粗糙度参数。基于仿真结果，ACF截断长度对仿真表面影响的机理可以归结为ACF截断形成的台阶不够小，从而导致相应的PSDF产生不可忽略的误差。此类误差将传播到模拟表面。为了避免ACF截断带来的不利影响，提出了一个保守的准则：自相关长度小于表面尺寸的8%，截断长度至少为自相关长度的7倍。结果表明，基于NCGM的MA模型在高频区域高估了模拟表面的PSDF值，这意味着模拟表面中存在显著的高频噪声。二维数字滤波方法和SRM方法具有几乎相同的性能，并且在满足ACF截断准则的情况下，两种方法都优于基于NCGM的MA模型。在大多数情况下，SRM生成的粗糙表面在粗糙度参数、ACF和PSDF方面的标准偏差最小，这意味着它可以在每次模拟时生成精确的表面，并且更稳定、更高效。因此，在所研究的三种方法中，SR是最推荐的方法。
Conventional methods for generating Gaussian random surfaces, including the moving average (MA) time series model with nonlinear conjugate gradient method (NCGM), two-dimensional (2-D) digital filter method, and spectral representation method (SRM), are implemented with a wide range of autocorrelation length and truncation length values of the autocorrelation function (ACF). The ACF, power spectral density function (PSDF), and essential roughness parameters of the simulated surfaces are calculated and compared. Based on the simulation results, the mechanism of the truncation length of ACF affecting the simulated surfaces can be summarized as that the step formed by truncating ACF is not sufficiently small, thus resulting in non-negligible errors in the corresponding PSDF. Such errors will be propagated to the simulated surfaces. A conservative criterion is proposed to avoid the adverse effects of truncating ACF: make the autocorrelation length less than 8% of the surface dimensions and the truncation length at least seven times autocorrelation length. The results show that the MA model with NCGM overestimates the PSDF values of simulated surfaces in the high-frequency region, meaning significant high-frequency noise in the simulated surfaces. The 2-D digital filter method and the SRM have almost the same performance, and both methods are better than the MA model with NCGM when the criterion of truncating ACF is fulfilled. The SRM generates rough surfaces with the smallest standard deviation in terms of the roughness parameters, ACF, and PSDF in most cases, meaning that it can generate accurate surfaces at every single simulation and is more stable and efficient. Therefore, the SRM is the most recommended method among the three methods studied.